For a class of Friedmann-Robertson-Walker-type string solutions with compact hyperbolic spatial slices formulated in the critical dimension, we find the world sheet conformal field theory which involves the linear dilaton and Wess-Zumino-Witten-type model with a compact hyperbolic target space. By analyzing the infrared spectrum, we conclude that the theory is actually supercritical due to modular invariance. Thus, taking into account previous results, we conclude that all simple nontrivial string cosmological solutions are in fact supercritical. In addition, we discuss the relationship of this background with the Supercritical String Cosmology (SSC).